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Calculating net force on four masses around a center mass?

  1. Apr 14, 2013 #1
    In the figure, a square of edge length 16.0 cm is formed by four spheres of masses m1 = 4.50 g, m2 = 2.80 g, m3 = 0.800 g, and m4 = 4.50 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.10 g?


    F = G (m1m2/r2)


    To get the radius as a diagonal I used pythagorean's theorem to calculate √162+162=11.31m.

    I've solved that the force on m1 due to the center particle is (6.67E-11)(4.50 x 2.10/11.312) = 4.93E-12.

    Solving the same way as above:

    force on m2: 3.06E-12

    force on m3: 8.76E-13

    force on m4: 4.93E-12 (same mass as m1)

    Was that the right radius to use in the law of universal gravitational equation?

    Now that I have those I don't know how to break them into unit vector notation and find the net force? Help please? Figure attached.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Apr 15, 2013 #2

    haruspex

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    Can you write down a unit vector pointing from the central mass to m1?
    Btw, you could have made things easier by recognising that each force has a factor mi, all else being the same. So you could have added up four vectors representing the four masses, then multiplied that by Gm5/(2d2)
     
  4. Apr 15, 2013 #3
    You'll need to use 8cm for this calculation instead of 16cm.

    Be careful with your units here. To get the force in N, you'll need to use SI units for the other quantities.
     
  5. Apr 15, 2013 #4
    Well what I don't know how to do is break up a diagonally pointing force into i and j components.

    And by "has a factor mi", do you mean that the j component of each force is the same? If so why is that? Would you just add up the four vectors' i components and multiply that by the equation you gave above?
     
  6. Apr 15, 2013 #5
    You just have to find the x- and y-components of the force. These are the i and j components.

    haruspex was just trying to save you some effort by noticing that all 4 force equations have a common term Gm5/r2
     
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